SOLUTION: Write the slope intercept equation for the line that passes through (2,-9) and (4,1).

Algebra ->  Linear-equations -> SOLUTION: Write the slope intercept equation for the line that passes through (2,-9) and (4,1).      Log On


   

Question 651929: Write the slope intercept equation for the line that passes through (2,-9) and (4,1).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=2 and y%5B1%5D=-9.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=1.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%281--9%29%2F%284-2%29 Plug in y%5B2%5D=1, y%5B1%5D=-9, x%5B2%5D=4, and x%5B1%5D=2


m=%2810%29%2F%284-2%29 Subtract -9 from 1 to get 10


m=%2810%29%2F%282%29 Subtract 2 from 4 to get 2


m=5 Reduce


So the slope of the line that goes through the points and is m=5


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--9=5%28x-2%29 Plug in m=5, x%5B1%5D=2, and y%5B1%5D=-9


y%2B9=5%28x-2%29 Rewrite y--9 as y%2B9


y%2B9=5x%2B5%28-2%29 Distribute


y%2B9=5x-10 Multiply


y=5x-10-9 Subtract 9 from both sides.


y=5x-19 Combine like terms.


So the equation that goes through the points and is y=5x-19